Assuming lepton flavour conservation, \(Z^\prime -W\)  boxes contribute to \(\tau \rightarrow \mu \,\nu _\tau \overline{\nu }_\mu \)  as [1]}
\(\begin{split}\frac{\mathcal {A}(\tau \rightarrow \mu \,\nu _\tau \overline{\nu }_\mu )}{\mathcal {A}(\tau \rightarrow \mu \,\nu _\tau \overline{\nu }_\mu )_{SM}}=&1-\frac{3}{8\pi ^2}\,g^{\ell L}_{22}\,g^{\ell L}_{33} \frac{\ln \left(\frac{m_W^2}{m_{Z^{\prime }}^2}\right)}{1-\frac{m_{Z^{\prime }}^2}{m_W^2}}\,,\end{split}\) 
